RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels

TL;DR

This paper establishes fundamental limits on the precision of estimating multiple parameters in quantum channels, showing that certain quantum advantages like Heisenberg scaling are unattainable under specific conditions.

Contribution

It proves a chain-rule inequality for RLD Fisher information, demonstrating that amortization does not increase information, leading to computable bounds on multiparameter quantum channel estimation.

Findings

Amortization does not increase RLD Fisher information.

Finite RLD Fisher information implies Heisenberg scaling is impossible.

Provides a fundamental, computable limit for multiparameter quantum estimation.

Abstract

One of the fundamental tasks in quantum metrology is to estimate multiple parameters embedded in a noisy process, i.e., a quantum channel. In this paper, we study fundamental limits to quantum channel estimation via the concept of amortization and the right logarithmic derivative (RLD) Fisher information value. Our key technical result is the proof of a chain-rule inequality for the RLD Fisher information value, which implies that amortization, i.e., access to a catalyst state family, does not increase the RLD Fisher information value of quantum channels. This technical result leads to a fundamental and efficiently computable limitation for multiparameter channel estimation in the sequential setting, in terms of the RLD Fisher information value. As a consequence, we conclude that if the RLD Fisher information value is finite, then Heisenberg scaling is unattainable in the multiparameter setting.